Abstract
AbstractWe construct a family of r‐graphs having a minimum 1‐factor cover of cardinality (disproving a conjecture of Bonisoli and Cariolaro, Birkhäuser, Basel, 2007, 73–84). Furthermore, we show the equivalence between the statement that is the best possible upper bound for the cardinality of a minimum 1‐factor cover of an r‐graph and the well‐known generalized Berge–Fulkerson conjecture.
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